This is difficult to answer. There are some techniques which allow you to find out, statistically, whether adding another parameter does anything more than "fitting the noise" - I don't have any reference handy (~20 years ago, I did a master thesis on a very related subject but that's long ago...), sorry.

However, you can also use your common sense. If you have way enough data, it should somehow be clear whether or not you get a big improvement in the fit when you add an extra parameter or not. Maybe some intuition about the model will tell you that too.
It is only when you are a bit low on data, or with noisy data, and not sure about your model (like in black box techniques), that these issues come up.
My former mechanics professor used to say: give me 12 parameters, and I give you an elephant. Give me one or two more, and I make his thrump sling about.